Answer: The measure of ∠E is 75°.
Step-by-step explanation: Given that DEFG is an isosceles trapezoid, where m∠D = 105° and m∠F = 75°.
We are to find the measure of ∠E.
ISOSCELES TRAPEZOID is a trapezoid in which the base angles are equal and so the left and right side lengths are also equal.
Therefore, in the isosceles trapezoid DEFG, we have
m∠D = m∠G, m∠E = m∠F and DE = FG.
Since, m∠D = 105°, so m∠G = 105°.
The sum of all the four angles of a quadrilateral is 360° and a trapezoid is a quadrilateral with a set of opposite parallel sides, so in the trapezoid DEFG, we have
[tex]m\angle D+m\angle E+m\angle F+m\ange G=360^\circ\\\\\Rightarrow 105^\circ+m\angle E+75^\circ+105^\circ=360^\circ\\\\\Rightarrow m\angle E+285^\circ=360^\circ\\\\\Rightarrow m\angle E=360^\circ-285^\circ\\\\\Rightarrow m\angle E=75^\circ.[/tex]
Thus, the measure of ∠E is 75°.
